Speaker: Aaron Hudson, Graduate Student, UW Biostatistics
Abstract: In biomedical applications, it is often of interest to study how the association among many variables in a population differs by sub-population membership. For example, an objective of many studies of functional brain connectivity is to determine how temporal dependence between physically distinct brain regions is differs between a population with a neurodegenerative disease and a healthy population. Commonly, practitioners assess for differential association by performing hypothesis tests for quantitative interactions – present when absolute differences in measures of association are non-zero. However, there are many settings in which quantitative interactions may not be clinically meaningful – for instance, when the units of the variables of interest are not interpretable. Alternatively, one may prefer to perform hypothesis tests for qualitative interactions – present when measures of association differ in sign. When a measure association is positive in population negative in another, we say a positive/negative interaction exists; when a measure of association is non-zero in one population and zero in another, we say an absence/presence interaction exists. Considerable work has been conducted to develop hypothesis tests for positive/negative interactions, though there is limited work on hypothesis testing for absence/presence interactions. Existing methods to test for absence/presence interactions require strong assumptions on minimum signal strength for type-I error control. To relax this strong assumption, we propose an alternative method which approximately tests for absence/presence interactions by testing the approximately equivalent null hypothesis that the relative difference in measures of association is bounded by a large pre-specified constant. Our proposed method ensures asymptotic type-I error control without minimum signal-strength assumptions. We compare our procedure to existing methods in simulations and apply our method to network inference in the analysis of resting state functional neuroimaging data.